A potential based panel method for 2-D hydrofoils (original) (raw)
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Performance analysis of 3D hydrofoil under free surface
Ocean Engineering, 2007
The purpose of the present paper is to develop a potential-based panel method for determining the steady potential flow about threedimensional hydrofoil under free surface. The method uses constant-strength doublets and source density distribution over the foil body surface and thereby Dirichlet-type boundary condition is used instead of Neumann-type condition. On the undisturbed free surface source density is used to meet the free surface condition that is linearised in terms of double-body model approach and is discretised by a one-side, upstream, four-point finite difference operator. After solving the doublets on the foil and sources on the free surface, the numerical results of pressure, lift and resistance coefficients and also wave profiles can then be calculated for different Froude number and depth of submergence to demonstrate the influence of free surface and aspect ratio effects on performance of the hydrofoil. r
Potential flow about two-dimensional hydrofoils
Journal of Fluid Mechanics, 1967
This paper describes a very general method for determining the steady two-dimensional potential flow about one or more bodies of arbitrary shape operating at arbitrary Froude number near a free surface. The boundary condition of zero velocity (solid wall) or prescribed velocity (suction or blowing) normal to the body surface is satisfied exactly, and the boundary condition of constant pressure on the free surface is satisfied using the classic small-wave approximation. Calculations made by the present method are compared with analytic results, other theoretical calculations and experimental data. Examples for which no comparison exists are also presented to illustrate the capability of the method.
Numerical Analysis of 2-D and 3-D Cavitating Hydrofoils Under a Free Surface
Journal of Ship Research
A method which models two- or three-dimensional cavitating hydrofoils moving with constant speed under a free surface is described. An integral equation is obtained by applying Green's theorem on all surfaces of the fluid domain. This integral equation is divided into two parts: (i) the cavitating hydrofoil problem, and (ii) the free-surface problem. These two problems are solved separately, with the effects of one on the other being accounted for in an iterative manner. The cavitating hydrofoil surface and the free surface are modeled with constant strength dipole and source panels. The source strengths on the free surface are expressed in terms of the second derivative of the potential with respect to the horizontal axis by applying the linearized free-surface conditions. The induced potential by the cavitating hydrofoil on the free surface and by the free surface on the hydrofoil are determined in an iterative sense. In order to prevent upstream waves the source strengths fro...
Second-Order Free Surface Effect on Cavitating 3-D Hydrofoils
The iterative method which is originally developed before for the three-dimensional cavitating hydrofoils moving with constant speed under a free surface is extended to include the second-order free surface effect into the calculations. The iterative nonlinear method is based on the Green's theorem and allows separating the cavitating hydrofoil problem and the free surface problem. These two problems are solved separately, with the effects of one on the other being accounted for in an iterative manner. The cavitating hydrofoil surface and the free surface are modeled with constant strength dipole and constant strength source panels. The second-order free surface effect is included into the calculations by the technique of small perturbation expansion both for the potential and for the wave elevation on the free surface. The source strengths on the free surface are expressed in terms of perturbation potential by applying first-order (linearized) and second-order free surface cond...
Effect of a Numerical Simulation of a Hydrofoil Near a Free Surface
Advances and Applications in Fluid Mechanics, 2017
Effect of a hydrofoil moving beneath a free surface is studied for several angles of attack for several speeds and submersion depths. In this study, NACA0012 foil is used. Finite volume method is both used for momentum and for k-ε equations where convective and diffusive terms are discretized, using QUICK and central schemes, respectively. Free surface is studied using volume-of-fluid method. Numerical results are also discussed.
Numerical and Physical Investigation of a Surface-Piercing Hydrofoil
The objective of this work is to extend a 3-D boundary element method for modeling the hydrodynamic response of a surface-piercing hydrofoil with consideration for the effects of cavitation and/or ventilation. The problem is formulated as a mixed boundary value problem for the perturbation velocity potential. The effect of the submerged depth based Froude number and ventilation on the cavity pressure is considered. The numerical predictions are compared with experimental measurements conducted at a free surface cavitation tunnel. The results show good comparisons between experimental measurements and numerical predictions in the base cavitating regime, when the cavity is closed to the free surface. When the cavity is open to the free surface, the pressure in the ventilated cavity, P c , varies between the vapor pressure (P v) and the absolute ambient pressure (P ) depending on the angle of attack, submergence, relative inflow velocity, difference between P and P v , and is influenced by hysteresis effects. Consequently, the lift coefficients vary significantly. The upper limit of the measured lift coefficients matched well with numerical predictions for P c =P v (fully attached or base cavitating regime), and the lower limit matched well with numerical predictions for P c =P (fully ventilated regime at very high Froude number and very low absolute ambient pressure).
EPJ Web of Conferences, 2015
Accurate simulation of turbulent free surface flows around surface ships has a central role in the optimal design of such naval vessels. The flow problem to be simulated is rich in complexity and poses many modeling challenges because of the existence of breaking waves around the ship hull, and because of the interaction of the two-phase flow with the turbulent boundary layer. In this paper, our goal is to estimate the lift and drag coefficients for NACA 0012 of hydrofoil advancing in calm water under steady conditions with free surface and emerged NACA 0015. The commercial CFD software FLUENT version 14 is used for the computations in the present study. The calculated grid is established using the code computer GAMBIT 2.3.26.The shear stress k-ȦSST model is used for turbulence modeling and the volume of fluid technique is employed to simulate the free-surface motion. In this computation, the second order upwind scheme is used for discretizing the convection terms in the momentum transport equations, the Modified HRIC scheme for VOF discretisation. The results obtained compare well with the experimental data.
NUMERICAL STUDY OF FREE SURFACE EFFECT ON THE FLOW AROUND SHALLOWLY SUBMERGED HYDROFOIL
buet.ac.bd
The wave generation due to the presence of a body moving at steady forward speed beneath a free surface has been the subject of extensive research work in marine hydrodynamics. In this study, the free surface effect on the flow around shallowly submerged hydrofoil is numerically computed. Finite Volume Method (FVM) based on Navier-Stokes equations is used for this purpose. The standard NACA 0012 hydrofoil section is used for ease of comparison with available experimental data. The k-ε turbulence model has been implemented to simulate turbulent flow past the foil surface. To get the free surface elevation, "Volume of Fluid" (VOF) method is incorporated in numerical simulation. Grid independency is checked using four grids of different sizes. To validate the computational results, the free surface wave generated by the flow around hydrofoil at submergence depth ratio h/c = 0.91 is compared with experimental results published by Duncan. The computed results show satisfactory agreement with the experimental measurements. Finally, free surface effects on wave profile are computed for six submergence depth ratios, h/c ranging from 0.911 to 4.0 and maximum amplitude at two different Froude nos. (F n = 0.5672 and 0.70)
Development of a hydrodynamic free surface capability in a low order aerodynamic panel method
13th Applied Aerodynamics Conference, 1995
The capability to analyze hydrodynamics in the presence of a free surface has been developed and implemented in the QUADPAN (QUADrilateral PANel) low order aerodynamic panel code. This method can be used in the analysis of seaborne aspects of seaplane performance, as well as more conventional watercraft, including ships and hydrofoils, traveling near or on the free surface. The development of this capability is described, a sensitivity study of various modeling parameters is presented, and a variety of two and three-dimensional results are presented. x Spatial position on X axis z Height above undisturbed free surface Potential (perturbation) p Doublet strength p Density a Source strength Subscripts a